Total Surface Area

Total Surface Area

8th grade Math

Thigpen/Neireiter

Total Surface Area

The surface area is the total area of all of a 3D shapes external faces.

We are working with rectangular prisms

These are 3D shapes. A solid (3-dimensional) object which has six faces that are rectangles. 

TSA=P(h)+2B

This is the formula we use to find total surface area of a rectangular prism.

TSA=P(h)+2B

• P = stands for the perimeter of the base

• B = stands for the area of the base

• h = stands for the distance between the two bases or the height of the prism

First Find P=Perimeter of the base

• For this example l=4 and w=3

• We know for a rectangle we will have 4 sides -2 lengths and 2 widths

• P=4+4+3+3

• P=14

Next find B=Area of the base

• We know the area of a square or rectangle = length x width

• for this example l=4 and w=3

• So B=4x3

• B=12

Now plug all your numbers in the formula: P(h)+2B

• We solved for P=14

• Then we solved for B=12

• we were given h=5

• Therefore TSA = 14(5)+2(12)

• Enter this into your calculator

TSA = 94 units²

*remember for surface area your units are squared

Open Ended

When will I need to use surface area?

*When you are asked to decide how much paper to use to wrap something.

*If you are asked how much paint you will need to paint the outside of an object.

*Any time they ask you about the packaging of a product.

All of the Above!

Now try to solve the following questions:

Multiple Choice

Find the Surface Area

• 556 cm²

• 278 cm²

• 680 cm²

• 340 cm²

Multiple Choice

Coach Hanf covered the outside of a gift box shaped like a rectangular prism with paper. The box is 3.2 feet long, 2.1 feet wide, and 2.7 feet high. Which of the following is closest to the total surface area of the box?

• 34 ft²

• 42 ft²

• 30 ft²

• 18 ft²

Multiple Choice

Mr. Murphy wants to build a shed with a floor like the one pictured. What is the amount of plywood he will need? (Include the floor, roof, and doors)

• 784 ft²

• 266 ft²

• 532 ft²

• 336 ft²

Multiple Choice

Find the surface area of the rectangular prism with the following dimensions: 
length = 11 m
height = 7 m
width = 2 m

• 226 m²
• 220 m²
• 150 m²
• 154 m²

Multiple Choice

Find the surface area of the rectangular prism with the following dimensions:

length = 11 m

height = 3 m

width = 1 m

• 226 m²

• 220 m²

• 150 m²

• 94 m²

Multiple Choice

What is the surface area of this figure?

• 200 cm ²

• 800 cm ²

• 400 cm ²

• 100 cm ²

Multiple Choice

A rectangular brick has a length of 5 centimeters, a width of  9 centimeters and a height of 20 centimeters. What is the surface area of that brick? 

• 650 cm²
• 600 cm²
• 525 cm²
• 450 cm²